Directory UMM :Data Elmu:jurnal:T:Tree Physiology:Vol16.1996:
Tree Physiology 16, 801--808
© 1996 Heron Publishing----Victoria, Canada
Evaluating a simple radiation/dry matter conversion model using data
from Eucalyptus globulus plantations in Western Australia
J. J. LANDSBERG1,3 and F. J. HINGSTON2
1
CSIRO Centre for Environmental Mechanics, Canberra, ACT 2601, Australia
2
CSIRO Divsion of Forestry, Wembley, WA 6014, Australia
3
Author to whom correspondence should be addressed
Received February 13, 1996
Summary A simple model that describes growth in terms of
physical and physiological processes is needed to predict
growth rates and hence the productivity of trees at particular
sites. The linear relationship expected between absorbed photosynthetically active radiation (ϕpa, MJ m −2) and dry mass
production (G(t)); i.e., G(t) = εϕpa, where ε is the radiation
utilization coefficient, was fitted to three years’ data from five
Western Australian Eucalyptus globulus Labill. plantations for
which monthly growth measurements, leaf area indices,
weather data and soil water measurements were available.
Reductions in growth efficiency relative to absorbed photosynthetically active radiation were associated with high vapor
pressure deficits (D, kPa) so the relationship between monthly
aboveground biomass increments and D was used to calculate
utilizable ϕpa. Plotting cumulative aboveground growth against
utilizable ϕpa gave strong linear relationships with slope ε.
Values of ε ranged from 0.93 to 2.23 g dry mass MJ −1 ϕpa. The
variation could not be explained either in terms of soil water
content in the root zones, because all plantations appeared to
have access to groundwater, or in terms of soil chemistry. A
value of ε ≈ 2.2 is considered near the maximum likely to be
applicable to Eucalyptus plantations. An interesting peripheral
finding was a strong relationship between allometric ratios and
soil phosphorus; this, if confirmed elsewhere, will be of considerable value in converting biomass increments to wood
production. There was also a strong negative relationship between the average ratio of leaf/total aboveground biomass and
soil nitrogen content.
Keywords: growth, productivity, radiation utilization efficiency, sustainable yield.
Introduction
Prediction of growth rates and hence of tree productivity at any
site is one of the central problems for forest managers, whether
they are concerned with plantations or the assessment of sustainable yields from natural forests. The solution to the problem has always been the use of conventional mensuration
models derived from measurements of trees in the field and
statistical descriptions of their size distributions and changes
in size over time. The problem with these models is that they
are completely empirical and site specific: they are essentially
descriptions of tree growth on particular sites subjected to a
particular range of weather conditions and management regimes; they cannot be used to evaluate the consequences of
different conditions or to estimate the likely productivity of
trees at sites where they do not grow, or have not been measured. To overcome these limitations we must develop models
that describe tree growth in terms of the physical environment
and physiological processes that govern growth.
Several such models have been developed in recent years
(see, for example, Running and Coughlan 1988, McMurtrie et
al. 1990, Wang and Jarvis 1990, Running and Gower 1991),
reflecting our improved knowledge of tree physiology and
ability to describe processes and interactions quantitatively.
However, these models are essentially research tools; they
require too many parameter values and weather data to be of
much value for forest management or for the wide-scale estimation of forest CO2 uptake and growth using, as input data,
information obtained by remote sensing. There is, therefore, a
need for a simple model, with few parameters, preferably with
robust, conservative values, that can be used by management
or easily applied to large areas. Such a model exists in the form
of a linear relationship between the radiant energy absorbed by
tree canopies and their rate of biomass production.
The change in rate of photosynthesis by a single leaf with
increasing photon flux density (PFD) is non-linear, but if a
canopy is closed, so that the foliage intercepts all, or most, of
the incident radiation, and much of the foliage is not PFD-saturated, photosynthesis by the canopy as a whole is likely to be
PFD-limited and the relationship between intercepted energy
and net photosynthesis by the canopy tends toward linearity.
This tendency is strengthened if a high proportion of incoming
radiation is diffuse. Non-linearities are also likely to be less
apparent over long periods (e.g., weeks, seasons) (Wang et al.
1992). The simple model may therefore be written
G (t) = ε∑ ϕ pa ,
(1)
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LANDSBERG AND HINGSTON
where G denotes net primary dry mass production, ε is the
radiation utilization efficiency coefficient and ϕpa denotes absorbed photosynthetically active radiation summed over some
time interval which, in the case of forests, is not likely to be
shorter than a month.
This relationship was first clearly identified by Monteith
(1977) for crops and orchards. Jarvis and Leverenz (1983)
demonstrated that it could be applied to forests, and Linder
(1985) provided the first empirical ε-values for forests.
Landsberg et al. (1996) have provided a review of the basis for
Equation 1, its implications and the range of values obtained
for ε in various studies. Unfortunately, the values of ε obtained
for trees are highly variable and the literature is likely to cause
confusion because ε-values have been expressed in terms of
photosynthetically active radiation (ϕp), total solar radiation
(ϕs) and both aboveground (Gb) and total dry mass production
(Gt). Because ϕp is approximately 0.5ϕs, values of ε obtained
in terms of absorbed solar radiation (ϕsa) will be about half
those obtained using ϕpa. Values for aboveground production,
in terms of ϕsa, range from ε =1.4 g dry mass MJ −1 for Salix
and Populus (Cannell et al. 1987, Cannell et al. 1988) to
0.43 g MJ −1 for several Eucalyptus species, including
E. globulus Labill. (Beadle and Inions 1990). Linder (1985)
calculated ε = 0.9 g MJ −1 ϕpa for young E. globulus stands in
Australia and 1.7 g MJ −1 ϕpa for aboveground production by
forest stands in Australia, New Zealand and Europe. Saldarriaga and Luxmoore (1991) obtained ε = 0.2 g MJ −1 ϕpa for
tropical rain forest stands at 23 sites in Colombia and Venezuela. (All analyses in this paper are in terms of ϕpa.)
Landsberg (1986) suggested that Equation 1 could be written in the form
G (t) = ε∑ ϕpa fθfD fT ,
(2)
where the modifying factors fi describe the effects of soil water
shortage (fθ), vapor pressure deficit acting on stomata (fD), and
temperature (fT). The modifiers would be non-dimensional,
with values between zero (no growth) and unity (no environmental constraints). They apply to the absorbed energy, modifying its effectiveness for growth. This approach was used by
Runyon et al. (1994) who applied modifiers based on environmental constraints (freezing temperatures, drought, vapor
pressure deficit) to the radiation intercepted by a range of plant
communities across an east--west transect in Oregon. The
modifiers improved the relationship between intercepted radiation and net primary productivity (NPP, see later comment
on definition); their analysis resulted in ε-values of 0.8 g MJ −1
ϕpa for aboveground NPP and 1.3 g MJ −1 for total NPP. All the
vegetation types studied fell on regression lines (NPP versus
ϕpa) that had r 2 values of 0.99. McMurtrie et al. (1994) used a
similar approach in a model-based study of gross primary
productivity (GPP) at five pine stands at locations ranging
from Sweden to Australia. In general, NPP is about one-third
of GPP because maintenance respiration of foliage and other
living biomass, plus the construction costs of new material,
consume about two-thirds of the carbohydrates fixed by photosynthesis. McMurtrie et al. (1994) improved the relationship
between GPP and ϕpa considerably by using environmental
modifiers to alter the effectiveness of radiation utilization.
When the modifiers have values less than unity they reduce the
amount of effective, or utilizable, radiation, which leads to
higher values of ε. In the case of the study by McMurtrie et al.
(1994), ε increased from 1.23 to 1.88.
This paper presents an analysis of growth data collected
from E. globulus plantations in Western Australia. The data
comprise five sets of continuous monthly measurements made
at separate sites over three years. They were collected primarily to allow evaluation of the performance of one of the detailed, mechanistic tree growth models mentioned earlier
(BIOMASS; McMurtrie et al. 1990), but offered the opportunity to test the applicability of the simple ε-model, to examine
environmental constraints on radiation utilization efficiency,
and to determine values for ε and examine how they varied.
Sites and measurements
Sites
Detailed descriptions of the plantations and site characteristics
are given by Hingston et al. (1995). Briefly, the five sites---called Darkan 87, Darkan 84 (the planting dates),
Mummbalup, Manjimup and Northcliffe----are located in the
south west of Western Australia, in a region with a characteristic Mediterranean-type climate, across a climatic gradient
with average annual rainfall ranging from about 600 to
1450 mm. Rooting depths were expected to be restricted to
about 1.5 m at Mummbalup, 3 m at the Darkan sites, 6 m at
Manjimup and up to 20 m at Northcliffe. Estimated total
available water when the root zones were wet was at least
200--250 mm in all cases. Neutron access tubes to 6 m at
Manjimup and Northcliffe indicated that water was extracted
to that depth.
Initial characteristics of the plantations at each site are given
in Table 1. The soils are moderately fertile (see Table 2) and
analysis of nutrient concentrations in foliage and wood supported the assumption that nutrition was not likely to be a
factor limiting tree growth.
Measurements
From February 1991 to July 1993, climatic variables were
continuously logged by automatic weather stations located
close to each of the sites. Rainfall, total incoming solar radiation and total utilizable ϕpa (see ‘Analysis and results’) over the
experimental period are given in Table 3. Monthly measurements were made of stem diameter (on 30 trees), leaf area
index (L*) (determined with a Li-Cor LI-2000 Canopy Analyzer, calibrated by biomass sampling and destructive leaf area
determinations) tree height and canopy depth. Leaf area index
fluctuated at all sites. The values at the beginning and end of
the experimental period are given in Table 1.
Litterfall was collected monthly. Soil water measurements
were made at all sites with a neutron probe from January 1992
onward and predawn leaf water potential measurements were
made on the same days.
RADIATION CONVERSION BY EUCALYPTUS
803
Table 1. Plantation characteristics.
Darkan
Darkan
Manjimup
Mummbalup
Northcliffe
Year
planted
Stocking
stems
ha −1
Tree
height
m
LAI
Feb
1991
LAI
July
1993
Standing
biomass
Mg ha−1
Standing
biomass
Mg ha−1
1987
1984
1984
1988
1986
680
430
680
1250
1250
7.2
14.5
25.0
8.8
16.3
0.5
2.5
5.0
2.5
6.0
3.2
3.5
4.0
4.2
6.0
17.4
48.8
109.6
19.9
129.5
57.6
75.5
151.4
75.6
225.6
Table 2. Soil conditions and values of ε for each plantation. The ε-values are those for the whole experimental period, based on utilizable ϕpa.
Darkan 87
Darkan 84
Manjimup
Mummbalup
Northcliffe
Bulk
density
Organic C%
0--10 cm
N%
0--10 cm
P (mg kg−1)
0--10 cm
P (mg kg −1)
10--25 cm
ε
values
1.7--2.2
1.4
1.3
-1--1.5
3.0
3.0
4.9
5.2
5.9
0.18
0.18
0.31
0.29
0.40
40
40
447
36
100
15
15
322
7
81
1.97
0.93
1.14
2.09
2.23
Table 3. Rainfall and radiation data for the experimental sites. Symbols: ϕs is total incoming solar radiation; ϕpa* is utilizable (corrected
for the effects of vapor pressure deficit) absorbed photosynthetically
active radiation.
Darkan 87
Darkan 84
Manjimup
Mummbalup
Northcliffe
Rainfall
1991
(mm)
Rainfall
1992
(mm)
ϕs Oct 1990
to July 1993
(MJ m −2)
ϕpa*
Total
(MJ m −2)
384
384
978
771
830
505
505
1118
801
1094
17521
17521
16731
15865
15008
1696
2413
3348
2570
3874
Several trees were felled at each site to establish the relationship between diameter at 1.3 m and total biomass, and the
relationships between stem, branch and foliage mass. Regressions were calculated so that the biomass components could be
estimated from the monthly stem diameter measurements.
Leaf mass was also estimated each month from the regressions,
constrained by the relationship with L*.
Analyses and results
Biomass increments (∆G) versus cumulative ϕpa
The normal procedure for determining values of ε is to plot
cumulative biomass (G(t)) against cumulative ϕpa( Σtϕpa). In
this case, cumulative biomass to any time was the standing
aboveground biomass at that time (Gb(t)) estimated from the
monthly stem diameter measurements and the regressions on
biomass components. A straight line relationship with slope ε
is expected. (Note that this definition of cumulative biomass is
not the same as NPP, which is normally defined as carbon fixed
minus autotrophic respiration. It would be difficult to obtain
good estimates of NPP from biomass sampling, because the
procedures would have to account for belowground turnover.
To estimate aboveground NPP litterfall must be included. Most
of the analyses presented here do not include litterfall, although its influence was evaluated (see ε values given in
Discussion)).
To calculate ϕpa, daily values of L* were estimated by
graphical interpolation between the values measured each
month, which were connected by continuous curves. Absorbed
photosynthetically active radiation, ϕpa, was calculated from
daily solar radiation on the assumption that photon absorption
is described by the widely used expression for exponential
extinction of light in canopies, so that
ϕpa = 0.5 ϕs (1 − exp (− kL∗)) .
(3)
We used k = 0.5 for all sites----a value unlikely to lead to serious
error (see Jarvis and Leverenz 1983). Note that Equations 1
or 2, and 3 account for the influence of leaf area, which need
not be considered further as a factor affecting growth.
The initial plots of Gb(t) against Σtϕpa (Figure1) yielded the
trends expected, but also revealed that, at each site, there were
quite long periods when growth was very slow. To investigate
the reasons for this, we plotted monthly biomass increments
(∆Gb) against the average air temperature for each month. The
data indicated that ∆Gb tended to decrease with increasing
temperature, which did not make biological sense for the range
of temperatures involved. We therefore investigated the effects
of vapor pressure deficit.
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LANDSBERG AND HINGSTON
Figure 1. Cumulative aboveground
biomass plotted against absorbed photosynthetically active radiation (ϕpa). The
data cover the experimental period at
each of the five sites. The open symbols
show the results obtained when ϕpa was
not corrected in any way: the points to
note are the ‘steps’ in the curves, indicating no biomass increment despite the absorption of large amounts of radiation.
When ϕpa was corrected for the effects of
vapor pressure deficit (Figure 2, and
text), to give utilizable radiation, the
linearity of the relationships was significantly improved (filled symbols). The εvalues noted on the diagrams were calculated from these (corrected) data.
Influence of vapor pressure deficit on growth
Vapor pressure deficit (D) is generally inversely related to air
temperature, and there is ample evidence in the physiological
literature that stomatal conductance in most plants is inversely
related to D (see Dye and Olbrich 1993; for results relating to
E. grandis W. Hill ex Maiden; Pereira et al. 1986, Pereira et al.
1987, for results relating to E. globulus). When stomata are
closed, leaves cannot absorb CO2 so growth must cease; therefore, high values of D would be expected to cause reductions
in growth. Dry mass increments in trees have not, to our
knowledge, previously been shown to be directly affected by
average vapor pressure deficits, although Myers et al. (1996)
Figure 2. Monthly biomass increments plotted against average
monthly vapor pressure deficit (D, kPa), derived from daily values.
Although there is considerable scatter, the relationship is good, when
we consider the errors in estimating monthly growth increments and
the number of factors that can influence them. The fitted curve has the
equation ∆Gb = 2.4(exp(− 1.88D)). Normalized, it gives the humidity
modifier: fD = 1.0(exp(− 1.88D)).
found a strong negative, non-linear relationship between annual stem volume increments in plantation eucalypts, and
average evaporation rates at various locations in Australia. We
calculated the daily average values of D from maximum and
minimum temperatures and the corresponding relative humidity data, and plotted ∆Gb against the average monthly values
of D. The result was a statistically significant inverse relationship (see Figure 2).
There is considerable scatter in Figure 2, but in view of the
number of factors other than vapor pressure deficit that contribute to variation in biomass increments, this is not surprising. To derive the modifier fD (Equation 2) we need to
normalize the relationship between ∆Gb and D, so that it has a
value of unity when D is small, i.e., where D has no effect.
Because of the scatter in the data, several formulations are
possible and will give results that are statistically indistiguishable. A linear relationship is the simplest, but leads to the
absurdity of negative values of ∆Gb when D gets high enough,
so we used a log-linear model, which is consistent with the
form of the relationship used by Dye and Olbrich (1993) (and
was a better fit than a linear relationship: r 2 = 0.29 versus
r 2 = 0.15). The resulting equation was ∆Gb = 2.4(exp (−1.88D)).
Normalizing this by dividing through by the intercept gives the
required equation for fD:
fD = 1.0 (exp(− 1.88D )).
(4)
For reference, Equation 4 gives values of fD = 0.7, 0. 5 and 0.22
for D = 0.2, 0.4 and 0.8 kPa, respectively. Using Equation 4,
daily values of fD were calculated and used to correct the daily
values of ϕpa. Total aboveground biomass was then plotted
RADIATION CONVERSION BY EUCALYPTUS
against cumulative values of Σt ϕpa fD, which gave relationships
with much improved linearity (see Figure 1). The ε-values on
the corrected ϕpa curves on Figure 1 (see also Table 3) were
calculated by linear regression (r 2 values were all > 0.98),
although simple graphical analysis gave essentially the same
values.
Soil water
We had intended to use soil water data to evaluate fθ (Equation 2). Daily values of total soil water content in the root zone
of each plantation were calculated using the water balance
routines in BIOMASS (see McMurtrie et al. 1990, McMurtrie
et al. 1992). For two of the plantations (Darkan 87 and
Mummbalup) the calculated values corresponded closely with
values measured with a neutron probe. For the Manjimup and
Northcliffe plantations there were periods----particularly when
805
extractable water was, according to the calculated balances,
largely depleted----when measured values were significantly
higher than calculated values. For the Darkan 84 plantation,
the correspondence between measured and calculated soil
water contents was poor.
To illustrate, we present the Darkan 87, Darkan 84 and
Northcliffe data in Figure 3. The higher measured than modeled water contents indicated that there was capillary rise from
the water tables into the root zone as the soils dried.
Unfortunately, the discrepancies between calculated and
measured soil water content, the known existence of water
tables at about 3 m depth at both the Darkan sites, and clear
evidence from neutron probe measurements of extraction
to 6 m at Manjimup and Northcliffe combine to make it impossible to obtain useful information about the effects of soil water
on the growth of these plantations. There was no evidence that
shortage of soil water was a major factor affecting the efficiency of utilization of absorbed radiation at any site: monthly
measurements of predawn leaf water potential (Ψpd), from
June 1992 March 1993 (inclusive), showed that, except for
February and March 1993 at Mummbalup, Ψpd never fell
below --1.3 MPa. (The two exceptions were --1.9 and --3.2
MPa, respectively.) We therefore conclude that, in general,
water stress was not a factor affecting the growth of these trees
and, even if it was, the differences between sites were not large
or consistent enough to allow useful comparative analyses.
This conclusion is supported by data presented by Dye (1996),
who found that E. grandis trees in South Africa could extract
water to at least 8 m depth, and showed no signs of stress until
Ψpd reached about − 2 MPa.
As another measure of the possible effects of soil water on
_growth, we calculated monthly average water deficit indices
Iθ for each site, based on measured water contents in the top
3 m, for the periods (n days) when soil water content was
measured by neutron probe. The formula used was
t
_
Iθ =
Figure 3. Simulated (continuous lines) and measured (dots) soil water
in the top 3 m of the profile at three of the experimental sites.
Simulations for the Darkan 87 site corresponded most closely with
measurements; the Darkan 84 results were the worst and the Manjimup and Mummbalup results were similar to those for Northcliffe.
These data indicated upward movement of water from water tables
during dry periods. Some measurements to 6 m depth also indicated
uptake from such depths. Soil water content was therefore of no value
as an explanation for site-to-site differences in ε (Figure 5).
∑ (θ − θmin ) ⁄ (θmax − θmin )
1
n
.
(5)
We took θmax = total available water (mm), determined from
neutron moisture meter measurements of maximum and minimum water contents in the root zones, and θmin = 0. Plotting
biomass increments against these values only indicated a relationship in the case of the Darkan 84 data, where monthly
biomass increments were inversely related to water deficit
indices. At the other sites, scatter in the data was such that no
clear relationship
could be identified. The overall average
_
values of Iθ for the last year of the experimental period ranged
from 0.37 to 0.49, with no indication of any relationship
between them and the ε-values calculated for the same period.
(These ε-values were not significantly different from those
obtained for the whole experimental period.) Therefore differences in soil water did not provide an explanation for differences in values of ε (i.e., fθ = 1).
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LANDSBERG AND HINGSTON
Soil chemistry
There was no apparent relationship between the chemical
properties of the soils and the growth rates and radiation
conversion efficiencies of the trees at these five sites. The soil
chemical properties are summarized in Table 3, which shows
the lack of any relationship with the ε-values. However, in
examining the influence of soil chemical properties on the
growth and growth patterns of the trees, we plotted the allometric ratios of stem to total biomass (ηs = Gstems/Gb) against the
natural logarithm of phosphorus content (mg kg −1) of the top
25 cm of soil. The result was Figure 4, which shows a remarkably strong relationship between ηs and soil P (r 2 = 0.85).
Although this does not explain the differences in ε, it is a
significant finding, and is discussed below. Hingston et al.
(1995), in their assessment of the performance of the model
BIOMASS in relation to these data, found that, to achieve
correspondence between modeled and measured aboveground
productivity, it was necessary to adjust the proportions of
assimilate allocated to stems and roots. The allometric ratios
for stems in relation to Gb varied from 0.5 to 0.7, but did not
vary systematically with stand age.
Discussion
This paper provides information about the values of the radiation utilization coefficient (ε) for aboveground growth and
about the influence of air humidity on growth. Because the
photosynthetically active radiation absorbed by the leaves was
corrected for the effects of air humidity on stomatal conductance to give a measure of utilizable radiation, the ε-values
resulting from the analysis will tend toward maximum achievable values, reflecting the capacity of the plant community to
produce biomass under optimum growing conditions. The
highest ε-values (for Mummbalup and Northcliffe) are near the
value of about 2.8 g MJ −1 ϕpa obtained by Cannell et al. (1987,
1988) for young Populus and Salix grown under unconstrained
conditions, suggesting that these values are nearing the maximum achievable for trees. When used in models to calculate
community productivity, maximum ε-values would be used
Figure 4. The allometric ratio (stem mass/total aboveground biomass)
as a function of ln(soil P). The relationship suggests that a higher
proportion of available carbohydrates is allocated to stems when
phosphorus is more readily available. (It is consistent with the common observation that more carbohydrate is allocated to roots in soils
where nutrition is poor.) There was no relationship between ε and soil
nutrient status.
and the modifiers applied to them----not to absorbed radiation----although the distinction is largely semantic because the
modifiers are multiplicative.
The low ε-values obtained from the Darkan 84 and Manjimup plantations indicate that there were factors limiting
radiation utilization by the trees in those plantations that we
have not been able to identify.
The ε-values obtained from this analysis (Figure1; Table 3)
are based on standing biomass, excluding litterfall, and are
higher than the values (about 0.9 and 0.8 g MJ −1 ϕpa) estimated
by Linder (1985) and by Beadle and Inions (1990), respectively (also excluding litterfall). The differences between our
values and theirs are easily accounted for by the corrections for
utilizable radiation that we made on the basis of the (inverse)
relationship between growth and vapor pressure deficits. Uncorrected values of ε would have been: Darkan 87, 0.76;
Darkan 84, 0.37; Manjimup, 0.58; Mummbalup, 0.92; Northcliffe, 1.23. When we include total litterfall over the experimental period, to give a true estimate of NPP, the ε-values
(utilizable radiation) are: Darkan ‘87, 2.34; Darkan ‘84, 1.18;
Manjimup, 1.44; Mummbalup, 2.48; Northcliffe, 2.73.
Although the effects of D on stomatal conductance, and
hence photosynthesis, are well documented, dry mass increments in trees have not previously been shown to be directly
affected by vapor pressure deficits. The results obtained in this
analysis are consistent with results from physiological studies
by Pereira et al. (1986), who showed that, in a similar climate
(Portugal), stomatal conductance and net photosynthesis in
E. globulus respond strongly to vapor pressure deficit. Pereira
et al. (1986) demonstrated seasonal effects on net photosynthesis, which was much higher in winter and spring than in
summer. We would expect the relationship between growth
and vapor pressure deficit to be influenced by differences in
respiration between sites and growth periods (see McMurtrie
et al. 1994) and by differences in carbon allocation patterns,
which would particularly affect aboveground growth patterns.
Nevertheless, the connection established in Figure 2, and its
effects on the linearity of the G b/Σϕpa relationship (Figure 1),
provide convincing evidence that vapor pressure deficits exert
first-order effects on the efficiency with which absorbed photosynthetically active radiation is converted to biomass, and
that ϕpa, and hence ε, should be corrected for these effects.
Soil water effects on radiation utilization efficiency may
operate over relatively long periods (weeks, seasons) by influencing leaf growth rates and, in severe drought conditions,
causing leaf shedding (see Pook 1986, Linder et al. 1987).
Over shorter periods (diurnal patterns) we would expect dry
soils to affect growth through effects on stomatal responses
and interactions with factors such as atmospheric humidity.
Direct measurements of stomatal conductance will be needed
to identify these (for an example, see the study by Tan et al.
1978). The underlying mechanism governing the soil water/atmospheric humidity effect on stomata must be the rate at which
water can move from the soil to the leaves of the trees: if the
atmospheric demand is strong (high D), flow rates to leaves are
not fast enough, regardless of soil water content, and the
stomata close. If they did not, the leaves would dry out. The
RADIATION CONVERSION BY EUCALYPTUS
Figure 5. The expected form of the soil water content × vapor pressure
modifier curves.
same effect would occur at low D when soil water content in
the root zone limits the rate at which water can move from soil
to leaves. The fθ term in Equation 2 is therefore likely to have
the form fθ = (1--exp(--bθ), where θ takes values between 0
and 1 (see Equation 4) and b would be expected to have a value
of about 3. The consequences of this formulation are illustrated
in Figure 5.
The generally good correspondence between measured and
simulated soil water contents in the Darkan 87 and
Mummbalup plantations, and in Manjimup and Northcliffe
from the time the rains came in May 1992, indicates that the
water balance calculations in the BIOMASS model can generally be accepted as accurate and will be useful as a basis for
calculating the probability of water shortages in many situations (see also McMurtrie et al. 1992). The model makes no
allowance for the presence of water tables, which appear to
account for the differences between measured and simulated
soil water content for some periods at some sites.
The lack of any obvious relationship between soil chemical
properties and productivity reflects the long-standing difficulty in forestry of predicting the effects of soil fertility (as
determined by conventional techniques) on tree growth rates
and productivity. The difficulty lies in the complexity of soil
chemistry per se, and the need to identify the chemical forms
taken up and used by plants, and in the fact that growth rates
are governed by the rate at which nutrients become available
to the trees from the soil. That rate is determined by nutrient
mineralization and organic matter turnover rates as much as by
the absolute amounts of nutrient present at any time. Effects of
soil chemistry on ε would be expected to operate through
mechanisms such as the influence of leaf nitrogen content on
maximum rates of leaf photosynthesis, although we found no
evidence in the literature that this mechanism operates in
eucalypts and no clear relationship between average leaf nitrogen content and ε-values emerged from this study.
The positive relationship between stem/total biomass ratio
(ηs) and soil P is important. It indicates that a higher proportion
of the carbon fixed by photosynthesis is allocated to the stems
of trees in relatively fertile soil than in less fertile soils. This is
consistent with the general (but not universal) finding that trees
growing in poor soils tend to allocate a greater proportion of
807
Figure 6. The allometric relationship (leaf mass/total aboveground
biomass) plotted against total soil N. As in the case of Figures 4 and 5,
the relationship is of value more as an indication of where to concentrate future investigations than as an explanation of the variation in ε
found in this analysis.
their carbon to roots than to aboveground biomass (see Linder
and Rook 1984, Beets and Whitehead 1996). These growth
responses to fertility suggest that the influence of nutrition on
tree growth and wood production observed in hundreds of
forest fertilization experiments may, in many cases, be as much
a consequence of altered carbon allocation patterns as of
changes in amounts of carbon fixed. Another result that
emerged from the analysis was a surprising inverse relationship between soil N and the foliage/total biomass ratio (ηf)
(Figure 6). This was also statistically highly significant
(r 2 = 0.58), despite the small number of points. It suggests that,
although improved nitrogen nutrition may result in increasing
leaf area, it may also result in increased partitioning of aboveground dry mass to stems, so that ηf falls. There was no
relationship between ηf and biomass production per se. The
form and coefficient values of the relationships between the
allometric ratios and soil nutrient status require confirmation
from other studies, but they are potentially helpful from the
point of view of predicting wood production because the values of the allometric ratios provide a means of estimating stem
production. The procedure would be to use Equation 2 to
calculate Gb(t), and use allometric ratios to calculate the mass
of the component parts (leaves, branches, stems).
In conclusion, we note that the analysis and results presented
here strengthen the case for the use of empirical values of ε in
models of forest productivity, and for the use of modifiers
based on environmental constraints, when these can be clearly
identified. Research in this area should focus on the translation
of knowledge about the effects of physiological processes on
growth into quantitative expressions of the influence of those
processes, integrated over intervals of months or seasons, on
biomass production. To identify and quantify such effects, it
will be necessary to carry out research using more sensitive
measures of growth than inferred biomass increments, with
measurements of stomatal conductance, leaf nitrogen dynamics and plant water relations.
We suggest that ε ≈ 2.2 g MJ −1 ϕpa is a good working value
for actively growing Eucalyptus plantations with adequate soil
water and nutrition. Equation 4 can be used to allow for the
effects of atmospheric humidity.
808
LANDSBERG AND HINGSTON
Acknowledgments
We thank Richard Waring for useful comments and discussion at the
review stage of this paper.
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© 1996 Heron Publishing----Victoria, Canada
Evaluating a simple radiation/dry matter conversion model using data
from Eucalyptus globulus plantations in Western Australia
J. J. LANDSBERG1,3 and F. J. HINGSTON2
1
CSIRO Centre for Environmental Mechanics, Canberra, ACT 2601, Australia
2
CSIRO Divsion of Forestry, Wembley, WA 6014, Australia
3
Author to whom correspondence should be addressed
Received February 13, 1996
Summary A simple model that describes growth in terms of
physical and physiological processes is needed to predict
growth rates and hence the productivity of trees at particular
sites. The linear relationship expected between absorbed photosynthetically active radiation (ϕpa, MJ m −2) and dry mass
production (G(t)); i.e., G(t) = εϕpa, where ε is the radiation
utilization coefficient, was fitted to three years’ data from five
Western Australian Eucalyptus globulus Labill. plantations for
which monthly growth measurements, leaf area indices,
weather data and soil water measurements were available.
Reductions in growth efficiency relative to absorbed photosynthetically active radiation were associated with high vapor
pressure deficits (D, kPa) so the relationship between monthly
aboveground biomass increments and D was used to calculate
utilizable ϕpa. Plotting cumulative aboveground growth against
utilizable ϕpa gave strong linear relationships with slope ε.
Values of ε ranged from 0.93 to 2.23 g dry mass MJ −1 ϕpa. The
variation could not be explained either in terms of soil water
content in the root zones, because all plantations appeared to
have access to groundwater, or in terms of soil chemistry. A
value of ε ≈ 2.2 is considered near the maximum likely to be
applicable to Eucalyptus plantations. An interesting peripheral
finding was a strong relationship between allometric ratios and
soil phosphorus; this, if confirmed elsewhere, will be of considerable value in converting biomass increments to wood
production. There was also a strong negative relationship between the average ratio of leaf/total aboveground biomass and
soil nitrogen content.
Keywords: growth, productivity, radiation utilization efficiency, sustainable yield.
Introduction
Prediction of growth rates and hence of tree productivity at any
site is one of the central problems for forest managers, whether
they are concerned with plantations or the assessment of sustainable yields from natural forests. The solution to the problem has always been the use of conventional mensuration
models derived from measurements of trees in the field and
statistical descriptions of their size distributions and changes
in size over time. The problem with these models is that they
are completely empirical and site specific: they are essentially
descriptions of tree growth on particular sites subjected to a
particular range of weather conditions and management regimes; they cannot be used to evaluate the consequences of
different conditions or to estimate the likely productivity of
trees at sites where they do not grow, or have not been measured. To overcome these limitations we must develop models
that describe tree growth in terms of the physical environment
and physiological processes that govern growth.
Several such models have been developed in recent years
(see, for example, Running and Coughlan 1988, McMurtrie et
al. 1990, Wang and Jarvis 1990, Running and Gower 1991),
reflecting our improved knowledge of tree physiology and
ability to describe processes and interactions quantitatively.
However, these models are essentially research tools; they
require too many parameter values and weather data to be of
much value for forest management or for the wide-scale estimation of forest CO2 uptake and growth using, as input data,
information obtained by remote sensing. There is, therefore, a
need for a simple model, with few parameters, preferably with
robust, conservative values, that can be used by management
or easily applied to large areas. Such a model exists in the form
of a linear relationship between the radiant energy absorbed by
tree canopies and their rate of biomass production.
The change in rate of photosynthesis by a single leaf with
increasing photon flux density (PFD) is non-linear, but if a
canopy is closed, so that the foliage intercepts all, or most, of
the incident radiation, and much of the foliage is not PFD-saturated, photosynthesis by the canopy as a whole is likely to be
PFD-limited and the relationship between intercepted energy
and net photosynthesis by the canopy tends toward linearity.
This tendency is strengthened if a high proportion of incoming
radiation is diffuse. Non-linearities are also likely to be less
apparent over long periods (e.g., weeks, seasons) (Wang et al.
1992). The simple model may therefore be written
G (t) = ε∑ ϕ pa ,
(1)
802
LANDSBERG AND HINGSTON
where G denotes net primary dry mass production, ε is the
radiation utilization efficiency coefficient and ϕpa denotes absorbed photosynthetically active radiation summed over some
time interval which, in the case of forests, is not likely to be
shorter than a month.
This relationship was first clearly identified by Monteith
(1977) for crops and orchards. Jarvis and Leverenz (1983)
demonstrated that it could be applied to forests, and Linder
(1985) provided the first empirical ε-values for forests.
Landsberg et al. (1996) have provided a review of the basis for
Equation 1, its implications and the range of values obtained
for ε in various studies. Unfortunately, the values of ε obtained
for trees are highly variable and the literature is likely to cause
confusion because ε-values have been expressed in terms of
photosynthetically active radiation (ϕp), total solar radiation
(ϕs) and both aboveground (Gb) and total dry mass production
(Gt). Because ϕp is approximately 0.5ϕs, values of ε obtained
in terms of absorbed solar radiation (ϕsa) will be about half
those obtained using ϕpa. Values for aboveground production,
in terms of ϕsa, range from ε =1.4 g dry mass MJ −1 for Salix
and Populus (Cannell et al. 1987, Cannell et al. 1988) to
0.43 g MJ −1 for several Eucalyptus species, including
E. globulus Labill. (Beadle and Inions 1990). Linder (1985)
calculated ε = 0.9 g MJ −1 ϕpa for young E. globulus stands in
Australia and 1.7 g MJ −1 ϕpa for aboveground production by
forest stands in Australia, New Zealand and Europe. Saldarriaga and Luxmoore (1991) obtained ε = 0.2 g MJ −1 ϕpa for
tropical rain forest stands at 23 sites in Colombia and Venezuela. (All analyses in this paper are in terms of ϕpa.)
Landsberg (1986) suggested that Equation 1 could be written in the form
G (t) = ε∑ ϕpa fθfD fT ,
(2)
where the modifying factors fi describe the effects of soil water
shortage (fθ), vapor pressure deficit acting on stomata (fD), and
temperature (fT). The modifiers would be non-dimensional,
with values between zero (no growth) and unity (no environmental constraints). They apply to the absorbed energy, modifying its effectiveness for growth. This approach was used by
Runyon et al. (1994) who applied modifiers based on environmental constraints (freezing temperatures, drought, vapor
pressure deficit) to the radiation intercepted by a range of plant
communities across an east--west transect in Oregon. The
modifiers improved the relationship between intercepted radiation and net primary productivity (NPP, see later comment
on definition); their analysis resulted in ε-values of 0.8 g MJ −1
ϕpa for aboveground NPP and 1.3 g MJ −1 for total NPP. All the
vegetation types studied fell on regression lines (NPP versus
ϕpa) that had r 2 values of 0.99. McMurtrie et al. (1994) used a
similar approach in a model-based study of gross primary
productivity (GPP) at five pine stands at locations ranging
from Sweden to Australia. In general, NPP is about one-third
of GPP because maintenance respiration of foliage and other
living biomass, plus the construction costs of new material,
consume about two-thirds of the carbohydrates fixed by photosynthesis. McMurtrie et al. (1994) improved the relationship
between GPP and ϕpa considerably by using environmental
modifiers to alter the effectiveness of radiation utilization.
When the modifiers have values less than unity they reduce the
amount of effective, or utilizable, radiation, which leads to
higher values of ε. In the case of the study by McMurtrie et al.
(1994), ε increased from 1.23 to 1.88.
This paper presents an analysis of growth data collected
from E. globulus plantations in Western Australia. The data
comprise five sets of continuous monthly measurements made
at separate sites over three years. They were collected primarily to allow evaluation of the performance of one of the detailed, mechanistic tree growth models mentioned earlier
(BIOMASS; McMurtrie et al. 1990), but offered the opportunity to test the applicability of the simple ε-model, to examine
environmental constraints on radiation utilization efficiency,
and to determine values for ε and examine how they varied.
Sites and measurements
Sites
Detailed descriptions of the plantations and site characteristics
are given by Hingston et al. (1995). Briefly, the five sites---called Darkan 87, Darkan 84 (the planting dates),
Mummbalup, Manjimup and Northcliffe----are located in the
south west of Western Australia, in a region with a characteristic Mediterranean-type climate, across a climatic gradient
with average annual rainfall ranging from about 600 to
1450 mm. Rooting depths were expected to be restricted to
about 1.5 m at Mummbalup, 3 m at the Darkan sites, 6 m at
Manjimup and up to 20 m at Northcliffe. Estimated total
available water when the root zones were wet was at least
200--250 mm in all cases. Neutron access tubes to 6 m at
Manjimup and Northcliffe indicated that water was extracted
to that depth.
Initial characteristics of the plantations at each site are given
in Table 1. The soils are moderately fertile (see Table 2) and
analysis of nutrient concentrations in foliage and wood supported the assumption that nutrition was not likely to be a
factor limiting tree growth.
Measurements
From February 1991 to July 1993, climatic variables were
continuously logged by automatic weather stations located
close to each of the sites. Rainfall, total incoming solar radiation and total utilizable ϕpa (see ‘Analysis and results’) over the
experimental period are given in Table 3. Monthly measurements were made of stem diameter (on 30 trees), leaf area
index (L*) (determined with a Li-Cor LI-2000 Canopy Analyzer, calibrated by biomass sampling and destructive leaf area
determinations) tree height and canopy depth. Leaf area index
fluctuated at all sites. The values at the beginning and end of
the experimental period are given in Table 1.
Litterfall was collected monthly. Soil water measurements
were made at all sites with a neutron probe from January 1992
onward and predawn leaf water potential measurements were
made on the same days.
RADIATION CONVERSION BY EUCALYPTUS
803
Table 1. Plantation characteristics.
Darkan
Darkan
Manjimup
Mummbalup
Northcliffe
Year
planted
Stocking
stems
ha −1
Tree
height
m
LAI
Feb
1991
LAI
July
1993
Standing
biomass
Mg ha−1
Standing
biomass
Mg ha−1
1987
1984
1984
1988
1986
680
430
680
1250
1250
7.2
14.5
25.0
8.8
16.3
0.5
2.5
5.0
2.5
6.0
3.2
3.5
4.0
4.2
6.0
17.4
48.8
109.6
19.9
129.5
57.6
75.5
151.4
75.6
225.6
Table 2. Soil conditions and values of ε for each plantation. The ε-values are those for the whole experimental period, based on utilizable ϕpa.
Darkan 87
Darkan 84
Manjimup
Mummbalup
Northcliffe
Bulk
density
Organic C%
0--10 cm
N%
0--10 cm
P (mg kg−1)
0--10 cm
P (mg kg −1)
10--25 cm
ε
values
1.7--2.2
1.4
1.3
-1--1.5
3.0
3.0
4.9
5.2
5.9
0.18
0.18
0.31
0.29
0.40
40
40
447
36
100
15
15
322
7
81
1.97
0.93
1.14
2.09
2.23
Table 3. Rainfall and radiation data for the experimental sites. Symbols: ϕs is total incoming solar radiation; ϕpa* is utilizable (corrected
for the effects of vapor pressure deficit) absorbed photosynthetically
active radiation.
Darkan 87
Darkan 84
Manjimup
Mummbalup
Northcliffe
Rainfall
1991
(mm)
Rainfall
1992
(mm)
ϕs Oct 1990
to July 1993
(MJ m −2)
ϕpa*
Total
(MJ m −2)
384
384
978
771
830
505
505
1118
801
1094
17521
17521
16731
15865
15008
1696
2413
3348
2570
3874
Several trees were felled at each site to establish the relationship between diameter at 1.3 m and total biomass, and the
relationships between stem, branch and foliage mass. Regressions were calculated so that the biomass components could be
estimated from the monthly stem diameter measurements.
Leaf mass was also estimated each month from the regressions,
constrained by the relationship with L*.
Analyses and results
Biomass increments (∆G) versus cumulative ϕpa
The normal procedure for determining values of ε is to plot
cumulative biomass (G(t)) against cumulative ϕpa( Σtϕpa). In
this case, cumulative biomass to any time was the standing
aboveground biomass at that time (Gb(t)) estimated from the
monthly stem diameter measurements and the regressions on
biomass components. A straight line relationship with slope ε
is expected. (Note that this definition of cumulative biomass is
not the same as NPP, which is normally defined as carbon fixed
minus autotrophic respiration. It would be difficult to obtain
good estimates of NPP from biomass sampling, because the
procedures would have to account for belowground turnover.
To estimate aboveground NPP litterfall must be included. Most
of the analyses presented here do not include litterfall, although its influence was evaluated (see ε values given in
Discussion)).
To calculate ϕpa, daily values of L* were estimated by
graphical interpolation between the values measured each
month, which were connected by continuous curves. Absorbed
photosynthetically active radiation, ϕpa, was calculated from
daily solar radiation on the assumption that photon absorption
is described by the widely used expression for exponential
extinction of light in canopies, so that
ϕpa = 0.5 ϕs (1 − exp (− kL∗)) .
(3)
We used k = 0.5 for all sites----a value unlikely to lead to serious
error (see Jarvis and Leverenz 1983). Note that Equations 1
or 2, and 3 account for the influence of leaf area, which need
not be considered further as a factor affecting growth.
The initial plots of Gb(t) against Σtϕpa (Figure1) yielded the
trends expected, but also revealed that, at each site, there were
quite long periods when growth was very slow. To investigate
the reasons for this, we plotted monthly biomass increments
(∆Gb) against the average air temperature for each month. The
data indicated that ∆Gb tended to decrease with increasing
temperature, which did not make biological sense for the range
of temperatures involved. We therefore investigated the effects
of vapor pressure deficit.
804
LANDSBERG AND HINGSTON
Figure 1. Cumulative aboveground
biomass plotted against absorbed photosynthetically active radiation (ϕpa). The
data cover the experimental period at
each of the five sites. The open symbols
show the results obtained when ϕpa was
not corrected in any way: the points to
note are the ‘steps’ in the curves, indicating no biomass increment despite the absorption of large amounts of radiation.
When ϕpa was corrected for the effects of
vapor pressure deficit (Figure 2, and
text), to give utilizable radiation, the
linearity of the relationships was significantly improved (filled symbols). The εvalues noted on the diagrams were calculated from these (corrected) data.
Influence of vapor pressure deficit on growth
Vapor pressure deficit (D) is generally inversely related to air
temperature, and there is ample evidence in the physiological
literature that stomatal conductance in most plants is inversely
related to D (see Dye and Olbrich 1993; for results relating to
E. grandis W. Hill ex Maiden; Pereira et al. 1986, Pereira et al.
1987, for results relating to E. globulus). When stomata are
closed, leaves cannot absorb CO2 so growth must cease; therefore, high values of D would be expected to cause reductions
in growth. Dry mass increments in trees have not, to our
knowledge, previously been shown to be directly affected by
average vapor pressure deficits, although Myers et al. (1996)
Figure 2. Monthly biomass increments plotted against average
monthly vapor pressure deficit (D, kPa), derived from daily values.
Although there is considerable scatter, the relationship is good, when
we consider the errors in estimating monthly growth increments and
the number of factors that can influence them. The fitted curve has the
equation ∆Gb = 2.4(exp(− 1.88D)). Normalized, it gives the humidity
modifier: fD = 1.0(exp(− 1.88D)).
found a strong negative, non-linear relationship between annual stem volume increments in plantation eucalypts, and
average evaporation rates at various locations in Australia. We
calculated the daily average values of D from maximum and
minimum temperatures and the corresponding relative humidity data, and plotted ∆Gb against the average monthly values
of D. The result was a statistically significant inverse relationship (see Figure 2).
There is considerable scatter in Figure 2, but in view of the
number of factors other than vapor pressure deficit that contribute to variation in biomass increments, this is not surprising. To derive the modifier fD (Equation 2) we need to
normalize the relationship between ∆Gb and D, so that it has a
value of unity when D is small, i.e., where D has no effect.
Because of the scatter in the data, several formulations are
possible and will give results that are statistically indistiguishable. A linear relationship is the simplest, but leads to the
absurdity of negative values of ∆Gb when D gets high enough,
so we used a log-linear model, which is consistent with the
form of the relationship used by Dye and Olbrich (1993) (and
was a better fit than a linear relationship: r 2 = 0.29 versus
r 2 = 0.15). The resulting equation was ∆Gb = 2.4(exp (−1.88D)).
Normalizing this by dividing through by the intercept gives the
required equation for fD:
fD = 1.0 (exp(− 1.88D )).
(4)
For reference, Equation 4 gives values of fD = 0.7, 0. 5 and 0.22
for D = 0.2, 0.4 and 0.8 kPa, respectively. Using Equation 4,
daily values of fD were calculated and used to correct the daily
values of ϕpa. Total aboveground biomass was then plotted
RADIATION CONVERSION BY EUCALYPTUS
against cumulative values of Σt ϕpa fD, which gave relationships
with much improved linearity (see Figure 1). The ε-values on
the corrected ϕpa curves on Figure 1 (see also Table 3) were
calculated by linear regression (r 2 values were all > 0.98),
although simple graphical analysis gave essentially the same
values.
Soil water
We had intended to use soil water data to evaluate fθ (Equation 2). Daily values of total soil water content in the root zone
of each plantation were calculated using the water balance
routines in BIOMASS (see McMurtrie et al. 1990, McMurtrie
et al. 1992). For two of the plantations (Darkan 87 and
Mummbalup) the calculated values corresponded closely with
values measured with a neutron probe. For the Manjimup and
Northcliffe plantations there were periods----particularly when
805
extractable water was, according to the calculated balances,
largely depleted----when measured values were significantly
higher than calculated values. For the Darkan 84 plantation,
the correspondence between measured and calculated soil
water contents was poor.
To illustrate, we present the Darkan 87, Darkan 84 and
Northcliffe data in Figure 3. The higher measured than modeled water contents indicated that there was capillary rise from
the water tables into the root zone as the soils dried.
Unfortunately, the discrepancies between calculated and
measured soil water content, the known existence of water
tables at about 3 m depth at both the Darkan sites, and clear
evidence from neutron probe measurements of extraction
to 6 m at Manjimup and Northcliffe combine to make it impossible to obtain useful information about the effects of soil water
on the growth of these plantations. There was no evidence that
shortage of soil water was a major factor affecting the efficiency of utilization of absorbed radiation at any site: monthly
measurements of predawn leaf water potential (Ψpd), from
June 1992 March 1993 (inclusive), showed that, except for
February and March 1993 at Mummbalup, Ψpd never fell
below --1.3 MPa. (The two exceptions were --1.9 and --3.2
MPa, respectively.) We therefore conclude that, in general,
water stress was not a factor affecting the growth of these trees
and, even if it was, the differences between sites were not large
or consistent enough to allow useful comparative analyses.
This conclusion is supported by data presented by Dye (1996),
who found that E. grandis trees in South Africa could extract
water to at least 8 m depth, and showed no signs of stress until
Ψpd reached about − 2 MPa.
As another measure of the possible effects of soil water on
_growth, we calculated monthly average water deficit indices
Iθ for each site, based on measured water contents in the top
3 m, for the periods (n days) when soil water content was
measured by neutron probe. The formula used was
t
_
Iθ =
Figure 3. Simulated (continuous lines) and measured (dots) soil water
in the top 3 m of the profile at three of the experimental sites.
Simulations for the Darkan 87 site corresponded most closely with
measurements; the Darkan 84 results were the worst and the Manjimup and Mummbalup results were similar to those for Northcliffe.
These data indicated upward movement of water from water tables
during dry periods. Some measurements to 6 m depth also indicated
uptake from such depths. Soil water content was therefore of no value
as an explanation for site-to-site differences in ε (Figure 5).
∑ (θ − θmin ) ⁄ (θmax − θmin )
1
n
.
(5)
We took θmax = total available water (mm), determined from
neutron moisture meter measurements of maximum and minimum water contents in the root zones, and θmin = 0. Plotting
biomass increments against these values only indicated a relationship in the case of the Darkan 84 data, where monthly
biomass increments were inversely related to water deficit
indices. At the other sites, scatter in the data was such that no
clear relationship
could be identified. The overall average
_
values of Iθ for the last year of the experimental period ranged
from 0.37 to 0.49, with no indication of any relationship
between them and the ε-values calculated for the same period.
(These ε-values were not significantly different from those
obtained for the whole experimental period.) Therefore differences in soil water did not provide an explanation for differences in values of ε (i.e., fθ = 1).
806
LANDSBERG AND HINGSTON
Soil chemistry
There was no apparent relationship between the chemical
properties of the soils and the growth rates and radiation
conversion efficiencies of the trees at these five sites. The soil
chemical properties are summarized in Table 3, which shows
the lack of any relationship with the ε-values. However, in
examining the influence of soil chemical properties on the
growth and growth patterns of the trees, we plotted the allometric ratios of stem to total biomass (ηs = Gstems/Gb) against the
natural logarithm of phosphorus content (mg kg −1) of the top
25 cm of soil. The result was Figure 4, which shows a remarkably strong relationship between ηs and soil P (r 2 = 0.85).
Although this does not explain the differences in ε, it is a
significant finding, and is discussed below. Hingston et al.
(1995), in their assessment of the performance of the model
BIOMASS in relation to these data, found that, to achieve
correspondence between modeled and measured aboveground
productivity, it was necessary to adjust the proportions of
assimilate allocated to stems and roots. The allometric ratios
for stems in relation to Gb varied from 0.5 to 0.7, but did not
vary systematically with stand age.
Discussion
This paper provides information about the values of the radiation utilization coefficient (ε) for aboveground growth and
about the influence of air humidity on growth. Because the
photosynthetically active radiation absorbed by the leaves was
corrected for the effects of air humidity on stomatal conductance to give a measure of utilizable radiation, the ε-values
resulting from the analysis will tend toward maximum achievable values, reflecting the capacity of the plant community to
produce biomass under optimum growing conditions. The
highest ε-values (for Mummbalup and Northcliffe) are near the
value of about 2.8 g MJ −1 ϕpa obtained by Cannell et al. (1987,
1988) for young Populus and Salix grown under unconstrained
conditions, suggesting that these values are nearing the maximum achievable for trees. When used in models to calculate
community productivity, maximum ε-values would be used
Figure 4. The allometric ratio (stem mass/total aboveground biomass)
as a function of ln(soil P). The relationship suggests that a higher
proportion of available carbohydrates is allocated to stems when
phosphorus is more readily available. (It is consistent with the common observation that more carbohydrate is allocated to roots in soils
where nutrition is poor.) There was no relationship between ε and soil
nutrient status.
and the modifiers applied to them----not to absorbed radiation----although the distinction is largely semantic because the
modifiers are multiplicative.
The low ε-values obtained from the Darkan 84 and Manjimup plantations indicate that there were factors limiting
radiation utilization by the trees in those plantations that we
have not been able to identify.
The ε-values obtained from this analysis (Figure1; Table 3)
are based on standing biomass, excluding litterfall, and are
higher than the values (about 0.9 and 0.8 g MJ −1 ϕpa) estimated
by Linder (1985) and by Beadle and Inions (1990), respectively (also excluding litterfall). The differences between our
values and theirs are easily accounted for by the corrections for
utilizable radiation that we made on the basis of the (inverse)
relationship between growth and vapor pressure deficits. Uncorrected values of ε would have been: Darkan 87, 0.76;
Darkan 84, 0.37; Manjimup, 0.58; Mummbalup, 0.92; Northcliffe, 1.23. When we include total litterfall over the experimental period, to give a true estimate of NPP, the ε-values
(utilizable radiation) are: Darkan ‘87, 2.34; Darkan ‘84, 1.18;
Manjimup, 1.44; Mummbalup, 2.48; Northcliffe, 2.73.
Although the effects of D on stomatal conductance, and
hence photosynthesis, are well documented, dry mass increments in trees have not previously been shown to be directly
affected by vapor pressure deficits. The results obtained in this
analysis are consistent with results from physiological studies
by Pereira et al. (1986), who showed that, in a similar climate
(Portugal), stomatal conductance and net photosynthesis in
E. globulus respond strongly to vapor pressure deficit. Pereira
et al. (1986) demonstrated seasonal effects on net photosynthesis, which was much higher in winter and spring than in
summer. We would expect the relationship between growth
and vapor pressure deficit to be influenced by differences in
respiration between sites and growth periods (see McMurtrie
et al. 1994) and by differences in carbon allocation patterns,
which would particularly affect aboveground growth patterns.
Nevertheless, the connection established in Figure 2, and its
effects on the linearity of the G b/Σϕpa relationship (Figure 1),
provide convincing evidence that vapor pressure deficits exert
first-order effects on the efficiency with which absorbed photosynthetically active radiation is converted to biomass, and
that ϕpa, and hence ε, should be corrected for these effects.
Soil water effects on radiation utilization efficiency may
operate over relatively long periods (weeks, seasons) by influencing leaf growth rates and, in severe drought conditions,
causing leaf shedding (see Pook 1986, Linder et al. 1987).
Over shorter periods (diurnal patterns) we would expect dry
soils to affect growth through effects on stomatal responses
and interactions with factors such as atmospheric humidity.
Direct measurements of stomatal conductance will be needed
to identify these (for an example, see the study by Tan et al.
1978). The underlying mechanism governing the soil water/atmospheric humidity effect on stomata must be the rate at which
water can move from the soil to the leaves of the trees: if the
atmospheric demand is strong (high D), flow rates to leaves are
not fast enough, regardless of soil water content, and the
stomata close. If they did not, the leaves would dry out. The
RADIATION CONVERSION BY EUCALYPTUS
Figure 5. The expected form of the soil water content × vapor pressure
modifier curves.
same effect would occur at low D when soil water content in
the root zone limits the rate at which water can move from soil
to leaves. The fθ term in Equation 2 is therefore likely to have
the form fθ = (1--exp(--bθ), where θ takes values between 0
and 1 (see Equation 4) and b would be expected to have a value
of about 3. The consequences of this formulation are illustrated
in Figure 5.
The generally good correspondence between measured and
simulated soil water contents in the Darkan 87 and
Mummbalup plantations, and in Manjimup and Northcliffe
from the time the rains came in May 1992, indicates that the
water balance calculations in the BIOMASS model can generally be accepted as accurate and will be useful as a basis for
calculating the probability of water shortages in many situations (see also McMurtrie et al. 1992). The model makes no
allowance for the presence of water tables, which appear to
account for the differences between measured and simulated
soil water content for some periods at some sites.
The lack of any obvious relationship between soil chemical
properties and productivity reflects the long-standing difficulty in forestry of predicting the effects of soil fertility (as
determined by conventional techniques) on tree growth rates
and productivity. The difficulty lies in the complexity of soil
chemistry per se, and the need to identify the chemical forms
taken up and used by plants, and in the fact that growth rates
are governed by the rate at which nutrients become available
to the trees from the soil. That rate is determined by nutrient
mineralization and organic matter turnover rates as much as by
the absolute amounts of nutrient present at any time. Effects of
soil chemistry on ε would be expected to operate through
mechanisms such as the influence of leaf nitrogen content on
maximum rates of leaf photosynthesis, although we found no
evidence in the literature that this mechanism operates in
eucalypts and no clear relationship between average leaf nitrogen content and ε-values emerged from this study.
The positive relationship between stem/total biomass ratio
(ηs) and soil P is important. It indicates that a higher proportion
of the carbon fixed by photosynthesis is allocated to the stems
of trees in relatively fertile soil than in less fertile soils. This is
consistent with the general (but not universal) finding that trees
growing in poor soils tend to allocate a greater proportion of
807
Figure 6. The allometric relationship (leaf mass/total aboveground
biomass) plotted against total soil N. As in the case of Figures 4 and 5,
the relationship is of value more as an indication of where to concentrate future investigations than as an explanation of the variation in ε
found in this analysis.
their carbon to roots than to aboveground biomass (see Linder
and Rook 1984, Beets and Whitehead 1996). These growth
responses to fertility suggest that the influence of nutrition on
tree growth and wood production observed in hundreds of
forest fertilization experiments may, in many cases, be as much
a consequence of altered carbon allocation patterns as of
changes in amounts of carbon fixed. Another result that
emerged from the analysis was a surprising inverse relationship between soil N and the foliage/total biomass ratio (ηf)
(Figure 6). This was also statistically highly significant
(r 2 = 0.58), despite the small number of points. It suggests that,
although improved nitrogen nutrition may result in increasing
leaf area, it may also result in increased partitioning of aboveground dry mass to stems, so that ηf falls. There was no
relationship between ηf and biomass production per se. The
form and coefficient values of the relationships between the
allometric ratios and soil nutrient status require confirmation
from other studies, but they are potentially helpful from the
point of view of predicting wood production because the values of the allometric ratios provide a means of estimating stem
production. The procedure would be to use Equation 2 to
calculate Gb(t), and use allometric ratios to calculate the mass
of the component parts (leaves, branches, stems).
In conclusion, we note that the analysis and results presented
here strengthen the case for the use of empirical values of ε in
models of forest productivity, and for the use of modifiers
based on environmental constraints, when these can be clearly
identified. Research in this area should focus on the translation
of knowledge about the effects of physiological processes on
growth into quantitative expressions of the influence of those
processes, integrated over intervals of months or seasons, on
biomass production. To identify and quantify such effects, it
will be necessary to carry out research using more sensitive
measures of growth than inferred biomass increments, with
measurements of stomatal conductance, leaf nitrogen dynamics and plant water relations.
We suggest that ε ≈ 2.2 g MJ −1 ϕpa is a good working value
for actively growing Eucalyptus plantations with adequate soil
water and nutrition. Equation 4 can be used to allow for the
effects of atmospheric humidity.
808
LANDSBERG AND HINGSTON
Acknowledgments
We thank Richard Waring for useful comments and discussion at the
review stage of this paper.
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